Applying efficient fault tolerance to enable the preconditioned conjugate gradient solver on approximate computing hardware

A new technique is presented that allows to execute the preconditioned conjugate gradient (PCG) solver on approximate hardware while ensuring correct solver results. This technique expands the scope of approximate computing to scientific and engineering applications. The changing error resilience of PCG during the solving process is exploited by different levels of approximation which trade off numerical precision and hardware utilization. Such approximation levels are determined at runtime by periodically estimating the error resilience. An efficient fault tolerance technique allows reductions in hardware utilization by ensuring the continued exploitation of suitable energy-precision trade-offs. Experimental results show that the hardware utilization is reduced on average by 14.5% and by up to 41.0% compared to executing PCG on precise hardware.